Question

A bouncy ball is dropped such that the height of its first bounce is 5.5 feet and each successive bounce is 64% of the previous bounce's height. What would be the height of the 7th bounce of the ball? Round to the nearest tenth (if necessary).

Answer 1

The height of the 7th bounce of a bouncy ball, when the first bounce is 5.5 feet and each subsequent bounce is 64% of the height of the previous bounce, is approximately 0.5 feet.

Step-by-step explanation:

The height of the 7th bounce of the ball can be determined by using the geometric series formula in which each term is 64% of the previous term. Given that the initial bounce height is 5.5 feet, we can multiply this height by 0.64 successively six times to find the height of the 7th bounce.

The height of the nth bounce is given by the formula:
Hn = H0 × (reduction factor)^(n-1)
where H0 is the initial height and the reduction factor in this case is 0.64.

So, the height of the 7th bounce H7 would be:
H7 = 5.5 × 0.64^6

Calculating this value we get:

H7 = 5.5 × 0.64^6 ≈ 0.5 feet (rounded to the nearest tenth).

The height of the 7th bounce is therefore approximately 0.5 feet.

Answer 2

0.4 ft

Step-by-step explanation:

It can be convenient to let a spreadsheet compute the values for you. Here, we have written an explicit formula for the height of the n-th bounce:

h = 5.5×0.64^(n-1)

We have written the formula this way because we are given the height of the first bounce, not the starting height. Each bounce multiplies the height by a factor of 0.64. Then the 7th bounce will have a height of ...

h = 5.5×0.64^6 ≈ 0.378 ≈ 0.4 . . . . feet